1. health and fitness
2. disease
3. aids and hiv

Package ‘HAC’
February 5, 2015
Type Package
Title Estimation, Simulation and Visualization of Hierarchical
Archimedean Copulae (HAC)
Version 1.0-2
Date 2014-08-14
Author Ostap Okhrin <[email protected]> and Alexander Ristig <[email protected]>
Maintainer Alexander Ristig <[email protected]>
LazyLoad yes
Depends R (>= 2.15.2), copula
Imports graphics
Description Package provides the estimation of the structure and the parameters, sampling methods and structural plots of Hierarchical Archimedean Copulae (HAC).
License GPL (>= 3)
URL https://www.wiwi.hu-berlin.de/professuren/quantitativ/statistik/members/
personalpages/o2
NeedsCompilation no
Repository CRAN
Date/Publication 2015-02-05 10:18:36
R topics documented:
aggregate.hac . . . .
copMult . . . . . . .
dHAC, pHAC, rHAC
emp.copula . . . . .
estimate.copula . . .
finData . . . . . . . .
get.params . . . . . .
hac . . . . . . . . . .
par.pairs . . . . . . .
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aggregate.hac
phi, phi.inv . . . .
plot.hac . . . . . .
theta2tau, tau2theta
to.logLik . . . . . .
tree2str . . . . . .
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Index
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aggregate.hac
Aggregation of variables
Description
aggregate tests, whether the absolute difference of the parameters of two subsequent nodes is
smaller than a constant, i.e. |θ2 − θ1 | < , where θi denotes the dependency parameter with
θ2 < θ1 , ≥ 0. If the absolute difference is smaller than the constant, the variables of the nodes
are aggregated in a single node with new dependency parameter, e.g. θnew = (θ1 + θ2 )/2. This
procedure is applied to all consecutive nodes of the HAC x.
Usage
## S3 method for class 'hac'
aggregate(x, epsilon = 0, method = "mean", ...)
Arguments
x
an object of the class hac.
epsilon
scalar ≥ 0.
method
determines, whether the new parameter is the "mean", "min" or "max" of the
fused parameters.
...
further arguments passed to or from other methods.
Value
an object of the class hac.
See Also
hac
Examples
# Example 1:
# an object of the class hac is constructed, whose parameters are close
copula = hac(type = 1, tree = list("X1", list("X2", "X3", 2.05), 2))
# the function aggregate returns a simple Archimedean copula
copMult
3
copula_ag = aggregate(copula, epsilon = 0.1)
tree2str(copula_ag) # [1] "(X1.X2.X3)_{2.02}"
# the structure does not change for a smaller epsilon
copula_ag = aggregate(copula, epsilon = 0.01)
tree2str(copula_ag) # [1] "((X2.X3)_{2.05}.X1)_{2}"
# Example 2:
# consider the binary tree
Object = hac.full(type = 1, y = c("X1", "X2", "X3", "X4", "X5"),
theta = c(1.01, 1.02, 2, 2.01))
tree2str(Object) # [1] "((((X5.X4)_{2.01}.X3)_{2}.X2)_{1.02}.X1)_{1.01}"
# applying aggregate.hac with epsilon = 0.02 leads to
Object_ag = aggregate(Object, 0.02)
tree2str(Object_ag) # [1] "((X3.X5.X4)_{2}.X1.X2)_{1.02}"
copMult
d-dim copula
Description
This function returns the values for d-dimensional Archimedean copulae.
Usage
copMult(X, theta, type)
Arguments
X
a n × d matrix, where d refers to the dimension of the copula.
theta
the parameter of the copula.
type
all copula-types produced by Archimedean generators, see phi for an overview
of implemented families.
Details
If warnings are returned, see phi.
Value
A vector containing the values of the copula.
4
dHAC, pHAC, rHAC
See Also
pHAC
Examples
# the arguments are defined
X = matrix(runif(300), ncol = 3)
# the values are computed
cop = copMult(X, theta = 1.5, type = 1)
dHAC, pHAC, rHAC
pdf, cdf and random sampling
Description
dHAC and pHAC compute the values of the copula’s density and cumulative distribution function
respectively. rHAC samples from HAC.
Usage
dHAC(X, hac, eval = TRUE, margins = NULL, na.rm = FALSE, ...)
pHAC(X, hac, margins = NULL, na.rm = FALSE, ...)
rHAC(n, hac)
Arguments
X
a data matrix. The number of columns and the corresponding names have to
coincide with the specifications of the copula model hac.
hac
an object of the class hac.
n
number of observations.
margins
specifies the margins. The data matrix X is assumed to contain the values of the
marginal distributions by default, i.e. margins = NULL. If raw data are used,
the margins can be determined nonparametrically, "edf", or in parametric way,
e.g. "norm". See estimate.copula for a detailed explanation.
na.rm
boolean. If na.rm = TRUE, missing values, NA, contained in X are removed.
eval
boolean. If eval = FALSE, a non-evaluated function is returned. Note, that
attr "gradient" of the returned function corresponds to the values density.
...
arguments to be passed to na.omit.
Details
Densities of simple Archimedean copula are based on the functions of the copula package.
dHAC, pHAC, rHAC
5
Value
rHAC retruns a n × d matrix, where d refers to the dimension of the HAC. dHAC and pHAC return
vectors. The computation of the density might be time consuming for high-dimensions, since the
density is defined as d-th derivative of the HAC with respect to its arguments u1 , . . . , ud .
References
Hofert, M. 2011, Efficiently Sampling Nested Archimedean Copulas, Computational Statistics &
Data Analysis 55, 57-70.
Joe, H. 1997, Multivariate Models and Dependence Concepts, Chapman & Hall.
McNeil, A. J. 2008, Sampling Nested Archimedean Copulas, Journal of Statistical Computation
and Simulation 78, 567-581.
Nelsen, R. B. 2006, An Introduction to Copulas, Spinger, 2nd Edition.
Okhrin, O. and Ristig, A. 2014, Hierarchical Archimedean Copulae: The HAC Package", Journal
of Statistical Software, 58(4), 1-20, http://www.jstatsoft.org/v58/i04/.
Savu, C. and Trede, M. 2010, Hierarchies of Archimedean copulas, Quantitative Finance 10, 295304.
See Also
estimate.copula, to.logLik
Examples
# AC example
# define the underlying model
model = hac(type = 4, tree = list("X1", "X2", 2))
# sample from model
sample = rHAC(100, model)
# returns the pdf/cdf at each vector of the sample
d.values = dHAC(sample, model)
p.values = pHAC(sample, model)
# HAC example
# the underlying model
y = c("X1", "X2", "X3")
theta = c(1.5, 3)
model = hac.full(type = 1, y, theta)
# define sample from copula model
sample = rHAC(100, model)
# returns the pdf/cdf at each point of the sample
d.values = dHAC(sample, model)
p.values = pHAC(sample, model)
# construct a hac-model
6
emp.copula
tree = list(list("X1", "X5", 3), list("X2", "X3", "X4", 4), 2)
model = hac(type = 1, tree = tree)
# sample from copula model
sample = rHAC(1000, model)
# check the accurancy of the estimation procedure
result1 = estimate.copula(sample)
result2 = estimate.copula(sample, epsilon = 0.2)
emp.copula
Empirical copula
Description
emp.copula and emp.copula.self compute the empirical copula for a given sample. The difference between these functions is, that emp.copula.self does not require a matrix u, at which the
function is evaluated.
Usage
emp.copula(u, x, proc = "M", sort = "none", margins = NULL,
na.rm = FALSE, ...)
emp.copula.self(x, proc = "M", sort = "none", margins = NULL,
na.rm = FALSE, ...)
Arguments
u
x
proc
sort
margins
na.rm
...
a matrix, at which the function is evaluated. According to the dimension of the
data matrix x, it can be a scalar, a vector or a matrix. The entries of u should be
within the interval [0, 1].
denotes the matrix of marginal distributions, if margins = NULL. The number of
columns should be equal the dimension d, whereas the number of rows should
be equal to the number of observations n, with n > d.
enables the user to choose between two different methods. It is recommended to
use the default method, "M", because it takes only a small fraction of the computational time of method "A". However, method "M" is sensitive with respect
to the size of the working memory and therefore, non-applicable for very large
datasets.
defines, whether the output is ordered. sort = "asc" refers to ascending values,
which might be interesting for plotting and sort = "desc" refers to descending
values.
specifies the margins. The data matrix is assumed to contain the values of the
marginal distributions by default, i.e. margins = NULL. If raw data are used,
the margins can be determined nonparametrically, "edf", or in parametric way,
e.g. "norm". See estimate.copula for a detailed explanation.
boolean. If na.rm = TRUE, missing values, NA, contained in x and u are removed.
arguments to be passed to na.omit.
estimate.copula
7
Details
The estimated copula follows the formula
b (u1 , . . . , ud ) = n−1
C
n Y
d
n
o
X
I Fbj (Xij ) ≤ uj ,
i=1 j=1
where Fbj denotes the empirical marginal distribution function of variable Xj .
Value
A vector containing the values of the empirical copula.
References
Okhrin, O. and Ristig, A. 2014, Hierarchical Archimedean Copulae: The HAC Package", Journal
of Statistical Software, 58(4), 1-20, http://www.jstatsoft.org/v58/i04/.
See Also
pHAC
Examples
v = seq(-4, 4, 0.05)
X = cbind(matrix(pt(v, 1), 161, 1), matrix(pnorm(v), 161, 1))
# both methods lead to the same result
z = emp.copula.self(X, proc = "M")
which(((emp.copula.self(X[1:100, ], proc = "M") - emp.copula.self(X[1:100, ],
proc = "A")) == 0) == "FALSE")
# integer(0)
# the contour plot
out = outer(z, z)
contour(x = X[,1], y = X[,2], out, main = "Contour Plot",
xlab = "Cauchy Margin", ylab = "Standard Normal Margin",
labcex = 1, lwd = 1.5, nlevels = 15)
estimate.copula
Estimation of Hierarchical Archimedean Copulae
Description
The function estimates the parameters and determines the structure of Hierarchical Archimedean
Copulae.
8
estimate.copula
Usage
estimate.copula(X, type = 1, method = 1, hac = NULL, epsilon = 0,
agg.method = "mean", margins = NULL, na.rm = FALSE, max.min = TRUE, ...)
Arguments
X
a n × d matrix. If there are no colnames provided, the names X1, X2, ... will
be given.
type
defines the copula family, see phi for an overview of implemented families.
method
the estimation method. Select between quasi Maximum Likelihood 1, full Maximum Likelihood 2 and recursive Maximum Likelihood 3.
hac
a hac object, which determines the structure and provides initial values. An object must be provided, if method = 2 referring to the full Maximum Likelihood
procedure.
epsilon
scalar ≥ 0. The variables of consecutive nodes are aggregated, if the difference
of the dependency parameters is smaller than epsilon. For a detailed explanation see also aggregate.hac.
agg.method
if > 0, the new dependency parameter can be determined by "mean", "min"
or "max" of the two parameters, see aggregate.hac.
margins
specifies the margins. The data matrix is assumed to contain the values of the
marginal distributions by default, i.e. margins = NULL. If raw data are used, the
margins can be determined nonparametrically, "edf", or in a parametric way,
e.g. "norm". Following the latter approach, the parameters of the distributions
are estimated by Maximum Likelihood. Building on these estimates the values
of the univariate margins are computed. If the argument is defined as scalar, all
margins are computed according to this specification. Otherwise, different margins can be defined, e.g. c("norm", "t", "edf") for a 3-dimensional sample.
Almost all continuous functions of Distributions are available. Inappropriate
usage of this argument might lead to misspecified margins, e.g. application of
"exp" even though the sample contains negative values.
na.rm
boolean. If na.rm = TRUE, missing values, NA, contained in X are removed.
max.min
boolean. If max.min = TRUE and an element of X is ≥ 1 or ≤ 0, it is set to
1 − 10−6 and 10−6 respectively.
...
further arguments passed to or from other methods, e.g. na.omit.
Value
A hac object is returned.
References
Genest, C., Ghoudi, K., and Rivest, L. P. 1995, A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of Distributions, Biometrika 82, 543-552.
Gorecki, J., Hofert, M. and Holena, M. 2014, On the Consistency of an Estimator for Hierarchical Archimedean Copulas, In Talaysova, J., Stoklasa, J., Talaysek, T. (Eds.) 32nd International
Conference on Mathematical Methods in Economics, Olomouc: Palacky University, 239-244.
finData
9
Joe, H. 2005, Asymptotic Efficiency of the Two-Stage Estimation Method for Copula-Based Models, Journal of Multivariate Analysis 94(2), 401-419.
Okhrin, O., Okhrin, Y. and Schmid, W. 2013, On the Structure and Estimation of Hierarchical
Archimedean Copulas, Journal of Econometrics 173, 189-204.
Okhrin, O. and Ristig, A. 2014, Hierarchical Archimedean Copulae: The HAC Package", Journal
of Statistical Software, 58(4), 1-20, http://www.jstatsoft.org/v58/i04/.
Examples
# define the copula model
tree = list(list("X1", "X5", 3), list("X2", "X3", "X4", 4), 2)
model = hac(type = 1, tree = tree)
# sample from copula model
x = rHAC(1000, model)
# in the following case the true model is binary approximated
est.obj = estimate.copula(x, type = 1, method = 1, epsilon = 0)
plot(est.obj)
# consider also the aggregation of the variables
est.obj = estimate.copula(x, type = 1, method = 1, epsilon = 0.2)
plot(est.obj)
# full ML estimation to yield more precise parameter
est.obj.full = estimate.copula(x, type = 1, method = 2, hac = est.obj)
# recursive ML estimation leads to almost identical results
est.obj.r = estimate.copula(x, type = 1, method = 3)
finData
Financial data
Description
This data set contains the standardized residuals of the filtered daily log-returns of four oil corporations: Chevron Corporation (CVX), Exxon Mobil Corporation (XOM), Royal Dutch Shell (RDSA)
and Total (FP), covering n = 283 observations from 2011-02-02 to 2012-03-19. Intertemporal dependence is removed by usual ARMA-GARCH models, whose standardized residuals are used as
finData.
Format
A matrix containing 283 observations of 4 stocks. The tickers of the stocks are presented as
colnames.
Source
Yahoo! Finance
10
get.params
Examples
# load the data
data(finData)
get.params
Dependency parameters of a HAC
Description
This function returns the copula parameter(s). They are ordered from top to down and left to right.
Usage
get.params(hac, sort.v = FALSE, ...)
Arguments
hac
an object of the class hac.
sort.v
boolean. If sort.v = TRUE, the output is sorted.
...
further arguments passed to sort.
See Also
tree2str
Examples
# construct a copula model
tree = list(list("X1", "X5", "X2", 4), list("X3", "X4", "X6", 3), 2)
model = hac(type = 1, tree)
# return the parameter
get.params(model) # [1] 2 4 3
get.params(model, sort.v = TRUE, decreasing = TRUE) # [1] 4 3 2
hac
11
hac
Construction of hac objects
Description
hac objects are required as input argument for several functions, e.g. plot.hac and rHAC. They can
be constructed by hac and hac.full. The latter function produces only fully nested Archimedean
copulae, whereas hac can construct arbitrary dependence structures for a given family. Moreover,
the functions hac2nacopula and nacopula2hac ensure the compatability with the copula package.
Usage
hac(type, tree)
hac.full(type, y, theta)
## S3 method for class 'hac'
print(x, digits = 2, ...)
hac2nacopula(x)
nacopula2hac(outer_nacopula)
Arguments
y
a vector containing the variables, which are denoted by a character, e.g. "X1".
theta
a vector containing the HAC parameters, which should be ordered from top to
down. The length of theta must be equal to length(y) - 1.
tree
a list object of the general structure list(..., numeric(1)). The last argument of the list, numeric(1), denotes the dependency parameter. The arguments
... are either of the same structure or of the class character. The character
objects denote variables and embedded lists refer to nested subcopulae.
type
all copula-types are admissible, see phi for an overview of implemented families.
x
a hac object.
outer_nacopula an nacopula object. The variables of the outer_nacopula object 1, 2, ...
are translated into the characters "X1", "X2", ....
digits
specifies the digits, see tree2str.
...
arguments to be passed to cat.
Value
A hac object is returned.
type
the specified copula type.
tree
the structure of the HAC.
12
par.pairs
References
Hofert, M. and Maechler, M. 2011, Nested Archimedean Copulas Meet R: The nacopula Package,
Journal of Statistical Software, 39(9), 1-20, http://www.jstatsoft.org/v39/i09/.
Hofert, M., Kojadinovic, I., Maechler, M. and Yan, J. 2013, copula: Multivariate Dependence with
Copulas, R package version 0.999-7, http://CRAN.R-project.org/package=copula.
Kojadinovic, I., Yan, J. 2010, Modeling Multivariate Distributions with Continuous Margins Using
the copula R Package, Journal of Statistical Software, 34(9), 1-20. http://www.jstatsoft.org/
v34/i09/.
Okhrin, O. and Ristig, A. 2014, Hierarchical Archimedean Copulae: The HAC Package", Journal
of Statistical Software, 58(4), 1-20, http://www.jstatsoft.org/v58/i04/.
Yan, J. 2007, Enjoy the Joy of Copulas: With a Package copula, Journal of Statistical Software,
21(4), 1-21, http://www.jstatsoft.org/v21/i04/.
Examples
# it might be helpful to plot the hac objects
# Example 1: 4-dim AC
tree = list("X1", "X2", "X3", "X4", 2)
AC = hac(type = 1, tree = tree)
# Example 2: 4-dim HAC
y = c("X1", "X4", "X3", "X2")
theta = c(2, 3, 4)
HAC1 = hac.full(type = 1, y = y, theta = theta)
HAC2 = hac(type = 1, tree = list(list(list("X2", "X3", 4),
"X4", 3), "X1", 2))
tree2str(HAC1) == tree2str(HAC2) # [1] TRUE
# Example 3: 9-dim HAC
HAC = hac(type = 1, tree = list("X6", "X5", list("X2", "X4", "X3", 4.4),
list("X1", "X7", 3.3), list("X8", "X9", 4), 2.3))
plot(HAC)
par.pairs
Parameter of the HAC
Description
This function returns a matrix of HAC parameters. They are pairwise ordered, so that the parameters
correspond to the lowest node, at which the variables are joined.
Usage
par.pairs(hac, FUN = NULL, ...)
phi, phi.inv
13
Arguments
hac
an object of the class hac.
FUN
the parameters of the HAC are returned by default. If FUN = "TAU", theta2tau
is applied to the parameters. FUN can also be a self-defined function.
...
further arguments passed to FUN.
See Also
get.params
Examples
# construct a copula model
tree = list(list("X1", "X5", "X2", 4), list("X3", "X4", "X6", 3), 2)
model = hac(type = 1, tree)
# returns the pairwise parameter
par.pairs(model)
# Kendall's TAU
par.pairs(model, FUN = "TAU")
# sqrt of the parameter
par.pairs(model, function(r)sqrt(r))
phi, phi.inv
Generator function
Description
The Archimedean generator function and its inverse.
Usage
phi(x, theta, type)
phi.inv(x, theta, type)
Arguments
x
a scalar, vector or matrix at which the function is evaluated. The support of the
functions has to be taken into account, i.e. x ∈ [0, ∞] for the generator function
and x ∈ [0, 1] for its inverse.
theta
the feasible copula parameter, i.e. θ ∈ [1, ∞) for the Gumbel and Joe family,
θ ∈ (0, ∞) for the Clayton and Frank family and θ ∈ [0, 1) for the Ali-MikhailHaq family.
type
select between the following integer numbers for specifying the type of the
hierarchical Archimedean copula (HAC) or Archimedean copula (AC):
14
plot.hac
•
•
•
•
•
•
•
•
•
•
1 = HAC Gumbel
2 = AC Gumbel
3 = HAC Clayton
4 = AC Clayton
5 = HAC Frank
6 = AC Frank
7 = HAC Joe
8 = AC Joe
9 = HAC Ali-Mikhail-Haq
10 = AC Ali-Mikhail-Haq
Examples
x = runif(100, min = 0, max = 100)
phi(x, theta = 1.2, type = 1)
# do not run
# phi(x, theta = 0.8, type = 1)
# In phi(x, theta = 0.8, type = 1) : theta >= 1 is required.
plot.hac
Plot of a HAC
Description
The function plots the structure of Hierarchical Archimedean Copulae.
Usage
## S3 method for class 'hac'
plot(x, xlim = NULL, ylim = NULL, xlab = "", ylab = "",
col = "black", fg = "black", bg = "white", col.t = "black", lwd = 2,
index = FALSE, numbering = FALSE, theta = TRUE, h = 0.4, l = 1.2,
circles = 0.25, digits = 2, ...)
Arguments
x
a hac object. It can be constructed by hac or be the result of estimate.copula.
xlim, ylim
numeric vectors of length 2, giving the limits of the x and y axes. The default
values adjust the size of the coordinate plane automatically with respect to the
dimension of the HAC.
xlab, ylab
titles for the x and y axes.
col
defines the color of the lines, which connect the circles and rectangles.
fg
defines the color of the lines of the rectangles and circles equivalent to the color
settings in R.
plot.hac
15
bg
defines the background color of the rectangles and circles equivalent to the color
settings in R.
col.t
defines the text color equivalent to the color settings in R.
lwd
the width of the lines.
index
boolean. If index = TRUE, strings, which illustrate the subcopulae of the nodes,
are used as subsrcipts of the dependency parameters.
numbering
boolean. If index = TRUE and numbering = TRUE, the dependency parameters
are numbered. If x is returned by estimate.copula, the numbers correpsond
to the estimation stages.
theta
boolean. Determines, whether the dependency parameter θ or Kendall’s rank
correlation coefficient τ is printed.
h
the height of the rectangles.
l
the width of the rectangles.
circles
a positive number giving the radius of the circles.
digits
an integer specifying the number of digits of the dependence parameter.
...
arguments to be passed to methods, e.g. graphical parameters (see par).
References
Okhrin, O. and Ristig, A. 2014, Hierarchical Archimedean Copulae: The HAC Package", Journal
of Statistical Software, 58(4), 1-20, http://www.jstatsoft.org/v58/i04/.
See Also
estimate.copula
Examples
# a hac object is created
tree = list(list("X1", "X5", 3), list("X2", "X3", "X4", 4), 2)
model = hac(type = 1, tree = tree)
plot(model)
# the same procedure works for an estimated object
sample = rHAC(2000, model)
est.obj = estimate.copula(sample, epsilon = 0.2)
plot(est.obj)
16
to.logLik
theta2tau, tau2theta
Kendall’s rank correlation coefficient
Description
Kendall’s rank correlation coefficient and its inverse.
Usage
theta2tau(theta, type)
tau2theta(tau, type)
Arguments
theta
the dependency parameter. It can be either a scalar, a vector or a matrix and has
to lie within a certain interval, i.e. θ ∈ [1, ∞) for the Gumbel and Joe family,
θ ∈ (0, ∞) for the Clayton and Frank family and θ ∈ [0, 1) for the Ali-MikhailHaq family.
tau
Kendall’s rank correlation coefficient. It can be either a scalar, a vector or a
matrix and it is to ensure, that τ ∈ [0, 1).
type
all types are available, see phi for an overview of implemented families.
Examples
# computation of the dependency parameter
x = runif(10)
theta = tau2theta(x, type = 1)
# computation of kendall's tau
y = runif(10, 1, 100)
tau = theta2tau(y, type = 1)
to.logLik
log-likelihood
Description
to.logLik returns either the log-likehood function depending on a vector theta for a given sample
X or the value of the log-likelihood, if eval = TRUE.
Usage
to.logLik(X, hac, eval = FALSE, margins = NULL, sum.log = TRUE,
na.rm = FALSE, ...)
tree2str
17
Arguments
X
a data matrix. The number of columns and the corresponding names have to
coincide with the specifications of the copula model hac. The sample X has to
contain at least 2 rows (observations), as the values of the underlying density
cannot be computed otherwise.
hac
an object of the class hac.
eval
boolean. If eval = FALSE, the non-evaluated log-likelihood function depending
on a parameter vector theta is returned and one default argument, the density,
is returned. The values of theta are increasingly ordered.
margins
specifies the margins. The data matrix X is assumed to contain the values of the
marginal distributions by default, i.e. margins = NULL. If raw data are used,
the margins can be determined nonparametrically, "edf", or in parametric way,
e.g. "norm". See estimate.copula for a detailed explanation.
sum.log
boolean. If sum.log = FALSE, the values of the individual log-likelihood contributions are returned.
na.rm
boolean. If na.rm = TRUE, missing values, NA, contained in X are removed.
...
arguments to be passed to na.omit.
See Also
dHAC
Examples
# construct a hac-model
tree = list(list("X1", "X5", 3), list("X2", "X3", "X4", 4), 2)
model = hac(type = 1, tree = tree)
# sample from copula model
sample = rHAC(1000, model)
# check the accurancy of the estimation procedure
ll = to.logLik(sample, model)
ll.value = to.logLik(sample, model, eval = TRUE)
ll(c(2, 3, 4)) == ll.value # [1] TRUE
tree2str
String structure of HAC
Description
The function prints the structure of HAC as string, so that the important characteristics of the copula
can be identified.
18
tree2str
Usage
tree2str(hac, theta = TRUE, digits = 2)
Arguments
hac
an object of the class hac.
theta
boolean. Determines, whether the values of the dependency parameter(s) are
printed (TRUE) or not (FALSE).
digits
a non-negative integer value specifying the number of digits of the dependency
parameter(s).
Value
a string of the class character.
See Also
plot.hac
Examples
# construct a hac object
tree = list(list("X1", "X5", "X2", 3), list("X3", "X4", "X6", 4), 2)
model = hac(type = 1, tree = tree)
# the parameters are returned within the curly brackets
# variables nested at the same node are separated by a dot
tree2str(model) # [1] "((X1.X5.X2)_{3}.(X3.X4.X6)_{4})_{2}"
# (X1.X5.X2)_{3} and (X3.X4.X6)_{4} are the two variables nested at the
# initial node with dependency parameter 2
tree2str(model, theta = FALSE) # [1] "((X1.X5.X2).(X3.X4.X6))"
# if theta = FALSE, only the structure of the variables is returned
# alternatively consider the following nested AC
tree = list("X1", list("X5", "X2", 3), list("X3", "X4", "X6", 4), 1.01)
model = hac(type = 1, tree = tree)
tree2str(model) # [1] "(X1.(X5.X2)_{3}.(X3.X4.X6)_{4})_{1.01}"
# _{1.01} represents the initial node
# the first three variables are given by the subtrees (X3.X4.X6)_{4},
# (X5.X2)_{3} and X1
Index
aggregate.hac, 2, 8
attr, 4
sort, 10
tau2theta (theta2tau, tau2theta), 16
theta2tau, 13
theta2tau (theta2tau, tau2theta), 16
theta2tau, tau2theta, 16
to.logLik, 5, 16
tree2str, 10, 11, 17
cat, 11
character, 11, 18
copMult, 3
dHAC, 17
dHAC (dHAC, pHAC, rHAC), 4
dHAC, pHAC, rHAC, 4
Distributions, 8
emp.copula, 6
estimate.copula, 4–6, 7, 14, 15, 17
finData, 9
function, 4, 13
get.params, 10, 13
hac, 2, 4, 8, 11, 14, 17
hac2nacopula (hac), 11
list, 11
na.omit, 4, 6, 8, 17
nacopula, 11
nacopula2hac (hac), 11
par, 15
par.pairs, 12
pHAC, 4, 7
pHAC (dHAC, pHAC, rHAC), 4
phi, 3, 8, 11, 16
phi (phi, phi.inv), 13
phi, phi.inv, 13
plot.hac, 11, 14, 18
print.hac (hac), 11
rHAC, 11
rHAC (dHAC, pHAC, rHAC), 4
19